Maximum and anti-maximum principles for the p-Laplacian with a nonlinear boundary condition
In this paper we study the maximum and the anti-maximum principles for the problem $Delta _{p}u=|u|^{p-2}u$ in the bounded smooth domain $Omega subset mathbb{R}^{N}$, with $|abla u|^{p-2}frac{partial u}{partial u }=lambda |u|^{p-2}u+h$ as a non linear boundary condition on $partial Omega $ which is...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2006-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/14/a8/abstr.html |
| Summary: | In this paper we study the maximum and the anti-maximum principles for the problem $Delta _{p}u=|u|^{p-2}u$ in the bounded smooth domain $Omega subset mathbb{R}^{N}$, with $|abla u|^{p-2}frac{partial u}{partial u }=lambda |u|^{p-2}u+h$ as a non linear boundary condition on $partial Omega $ which is supposed $C^{2eta }$ for some $eta $ in $]0,1[$, and where $hin L^{infty }(partial Omega )$. We will also examine the existence and the non existence of the solutions and their signs. |
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| ISSN: | 1072-6691 |